Produced in nuclear processes (e.g. fusion reactions) Solar neutrinos and supernova neutrinos

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3 Sources of Neutrinos Low energy neutrinos (10 th of MeV) Produced in nuclear processes (e.g. fusion reactions) Solar neutrinos and supernova neutrinos High energy neutrinos (10 th of GeV) Produced in high energy particle collisions short-lived mesons Unknown sources of high energy cosmic rays Almost the same direction as the incoming neutrino Giving the direction of muon neutrino: Key to understanding high energy neutrino astronomy

4 5 Evidence at IceCube Introduction Cur vatur eradiation Synchr otron emission Outlook Neutrino sources Low energy: 10 6 ev Big Bang Radioactive decays Reactors, fusion IceTop IceCube Air shower detector threshold ~ 300 TeV : : 13 Strings total of 40 Strings : 8 Strings High energy: 10 9 ev Cosmic rays in the atmosphere Active galatic nuclei (AGN) Magnetars -ray burst (GRB) At the neutrino interaction point (bottom), a large particle shower is visible, with a muon produced in the interaction leaving up and to the left. InIce Strings, 60 Optical Modules 17 m between Modules 125 m between Strings : 1 String first data 2005 upgoing muon 18. July 18, 2005 AMANDA 19 Strings 677 Modules IceCube Coll., Science 342 (2013) 6161, IceCube can detect neutrinos of ev Figure 2 IceCube Neutrino telescope at the south pole

5 Idea on the Neutrino Source Strong magnetic field Related to the unknown origin of the kick velocity. Rothchild et al., Nature 368 (1994), 432 Magnetars as an acceleration site for ultra-high energy cosmic rays (UHECRs). Ioka et al., Astrophys. J. 633 (2005), 1013 Synchrotron-type radiation Strong coupling of proton to meson fields, High energy protons can radiate pions in a strong magnetic field. Charged particle

6 Early Attempts Semiclassical approaches Ginzburg & Zharkov (1964), Tokuhisa & Kajino (1999), Herpay & Patkos (2007) Hadronic matrix No explicit contribution of magnetic fields

7 Early Attempts Semiclassical approaches Tokuhisa & Kajino, Astrophys. J. 525 (1999), L117 Energy spectra of neutral pion emission and photon synchrotron radiation for various proton energies with fixed magnetic field of 1.5 X G.

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9 Quantum Approach Dirac equation A=(0, 0, xb, 0) Wave function Anomalous magnetic moment Energy eigenvalue Landau levels

10 Quantum Approach Pion production Decay width Proton self-energy Proton propagator Pion propagator

11 Decay Width Proton propagator Decay width of a 1 GeV proton by the synchrotron emission in the fixed magnetic field of 5 X G. Comparison with semi-classical results

12 Decay Width Contributions from the final Landau level Proton propagator Pionic decay widths of proton (a1), (b1) and the pion transverse momenta (a2), (b2). The initial Landau number is fixed to be n i +(1-s i )/2=45.

13 Differential Decay Width Angular distribution Proton propagator

14 Differential Decay Width Initial and final spin dependence Proton propagator The differential pionic decay widths of protons (a) with and (b) without the AMM included. The widths are averaged over initial Landau numbers.

15 Differential Decay Width Pion energy dependence Proton propagator The dependence of the proton decay width on the pion energy for a magnetic field of 5 X G. The solid and dashed lines represent the results with and without the AMM. The pion energy dependence of the proton decay width when proton energy is 1 GeV.

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17 Summary Proton propagator We have calculated the pionic synchrotron radiation in a fully quantum field theoretical way. The anomalous magnetic moment (AMM) has a very large effect which enlarges the emission rate. The AMM effect becomes larger as the magnetic field decreases. Calculations of the neutrino production are in progress. Discussion Schwinger representation Valid in the weak limit of the magnetic field. Can overestimate the AMM effect in such a huge magnetic field strength. Magnetars Fast rotation and strong magnetic field Curvature radiation

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